The above applies directly when the term is used in mathematics, philosophy, literature, or linguistics. For example, if there is a concept A, and it is split into parts B and not-B, then the parts form a dichotomy: they are mutually exclusive, since no part of B is contained in not-B and vice versa, and they are jointly exhaustive, since they cover all of A, and together again give A.

In set theory, a dichotomous relation R is such that either aRb, bRa, but not both.[1]

A false dichotomy is an informal fallacy consisting of a supposed dichotomy which fails one or both of the conditions: it is not jointly exhaustive and/or not mutually exclusive. In its most common form, two entities are presented as if they are exhaustive, when in fact other alternatives are possible. In some cases, they may be presented as if they are mutually exclusive although there is a broad middle ground (see also undistributed middle).

In economics, the classical dichotomy is the division between the real side of the economy and the monetary side. According to the classical dichotomy, changes in monetary variables do not affect real values such as output, employment, and the real interest rate. Money is therefore neutral in the sense that its quantity cannot affect these real variables.

In biology, a dichotomy is a division of organisms into two groups, typically based on a characteristic present in one group and absent in the other. Such dichotomies are used as part of the process of identifying species, as part of a dichotomous key, which asks a series of questions, each of which narrows down the set of organisms. A well known dichotomy is the question "does it have a backbone?" used to divide species into vertebrates and invertebrates.

In botany, a dichotomy is a mode of branching by repeated bifurcation - thus a focus on branching rather than on division

In computer science, more specifically in programming-language engineering, the term dichotomy can denote fundamental dualities in a language's design. For instance, C++ has a dichotomy in its memory model (heap versus stack), whereas Java has a dichotomy in its type system (references versus primitive data types).

Perceived dichotomies are common in Western thought. C. P. Snow believes that Western society has become an argument culture (The Two Cultures). In The Argument Culture (1998), Deborah Tannen suggests that the dialogue of Western culture is characterized by a warlike atmosphere in which the winning side has truth (like a trophy). Such a dialogue virtually ignores the middle alternatives.

The I Ching and taijitu represent the yin yang theories of traditional Chinese culture. However, these do not represent a true dichotomy as the symbol incorporates a portion of each in the other, representing a dialectic.